LU Decomposition. More...
#include <Bpp/Numeric/Matrix/LUDecomposition.h>
Collaboration diagram for bpp::LUDecomposition< Real >:
Public Member Functions | |
| LUDecomposition (const Matrix< Real > &A) | |
| LU Decomposition. More... | |
| const RowMatrix< Real > & | getL () |
| Return lower triangular factor. More... | |
| const RowMatrix< Real > & | getU () |
| Return upper triangular factor. More... | |
| std::vector< size_t > | getPivot () const |
| Return pivot permutation vector. More... | |
| Real | det () const |
| Compute determinant using LU factors. More... | |
| Real | solve (const Matrix< Real > &B, Matrix< Real > &X) const |
| Solve A*X = B. More... | |
| Real | solve (const std::vector< Real > &b, std::vector< Real > &x) const |
| Solve A*x = b, where x and b are vectors of length equal to the number of rows in A. More... | |
Static Private Member Functions | |
| static void | permuteCopy (const Matrix< Real > &A, const std::vector< size_t > &piv, size_t j0, size_t j1, Matrix< Real > &X) |
| static void | permuteCopy (const std::vector< Real > &A, const std::vector< size_t > &piv, std::vector< Real > &X) |
Private Attributes | |
| RowMatrix< Real > | LU |
| RowMatrix< Real > | L_ |
| RowMatrix< Real > | U_ |
| size_t | m |
| size_t | n |
| int | pivsign |
| std::vector< size_t > | piv |
Detailed Description
template<class Real>
class bpp::LUDecomposition< Real >
LU Decomposition.
[This class and its documentation is adpated from the C++ port of the JAMA library.]
For an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n unit lower triangular matrix L, an n-by-n upper triangular matrix U, and a permutation vector piv of length m so that A(piv,:) = L*U. If m < n, then L is m-by-m and U is m-by-n.
The LU decompostion with pivoting always exists, even if the matrix is singular, so the constructor will never fail. The primary use of the LU decomposition is in the solution of square systems of simultaneous linear equations. This will fail if isNonsingular() returns false.
Definition at line 72 of file LUDecomposition.h.
Constructor & Destructor Documentation
◆ LUDecomposition()
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inline |
LU Decomposition.
- Parameters
-
A Rectangular matrix
- Returns
- LU Decomposition object to access L, U and piv.
Definition at line 197 of file LUDecomposition.h.
References bpp::LUDecomposition< Real >::LU, bpp::LUDecomposition< Real >::m, bpp::LUDecomposition< Real >::n, bpp::LUDecomposition< Real >::piv, and bpp::LUDecomposition< Real >::pivsign.
Member Function Documentation
◆ det()
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inline |
Compute determinant using LU factors.
- Returns
- determinant of A, or 0 if A is not square.
Definition at line 315 of file LUDecomposition.h.
References bpp::LUDecomposition< Real >::LU, bpp::LUDecomposition< Real >::m, bpp::LUDecomposition< Real >::n, and bpp::LUDecomposition< Real >::pivsign.
Referenced by bpp::MatrixTools::det().
◆ getL()
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inline |
Return lower triangular factor.
- Returns
- L
Definition at line 252 of file LUDecomposition.h.
References bpp::LUDecomposition< Real >::L_, bpp::LUDecomposition< Real >::LU, bpp::LUDecomposition< Real >::m, and bpp::LUDecomposition< Real >::n.
◆ getPivot()
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inline |
Return pivot permutation vector.
- Returns
- piv
Definition at line 304 of file LUDecomposition.h.
References bpp::LUDecomposition< Real >::piv.
◆ getU()
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inline |
Return upper triangular factor.
- Returns
- U portion of LU factorization.
Definition at line 280 of file LUDecomposition.h.
References bpp::LUDecomposition< Real >::LU, bpp::LUDecomposition< Real >::n, and bpp::LUDecomposition< Real >::U_.
◆ permuteCopy() [1/2]
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inlinestaticprivate |
Definition at line 84 of file LUDecomposition.h.
References bpp::LUDecomposition< Real >::piv, and bpp::Matrix< Scalar >::resize().
Referenced by bpp::LUDecomposition< Real >::solve().
◆ permuteCopy() [2/2]
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inlinestaticprivate |
Definition at line 99 of file LUDecomposition.h.
References bpp::LUDecomposition< Real >::piv.
◆ solve() [1/2]
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inline |
Solve A*X = B.
- Parameters
-
B [in] A Matrix with as many rows as A and any number of columns. X [out] A RowMatrix that will be changed such that L*U*X = B(piv,:).
- Returns
- the lowest diagonal term (in absolute value), for further checkings of non-singularity of LU.
If B is nonconformant or LU is singular, an Exception is raised.
Definition at line 340 of file LUDecomposition.h.
References bpp::Matrix< Scalar >::getNumberOfColumns(), bpp::Matrix< Scalar >::getNumberOfRows(), bpp::LUDecomposition< Real >::LU, bpp::LUDecomposition< Real >::m, bpp::LUDecomposition< Real >::n, bpp::LUDecomposition< Real >::permuteCopy(), bpp::LUDecomposition< Real >::piv, and bpp::NumConstants::SMALL().
Referenced by bpp::MatrixTools::inv().
◆ solve() [2/2]
|
inline |
Solve A*x = b, where x and b are vectors of length equal to the number of rows in A.
- Parameters
-
b [in] a vector (Array1D> of length equal to the first dimension of A. x [out] a vector that will be changed so that so that L*U*x = b(piv).
- Returns
- the lowest diagonal term (in absolute value), for further checkings of non-singularity of LU.
If B is nonconformant or LU is singular, an Exception is raised.
Definition at line 414 of file LUDecomposition.h.
References bpp::LUDecomposition< Real >::LU, bpp::LUDecomposition< Real >::m, bpp::LUDecomposition< Real >::n, bpp::LUDecomposition< Real >::permuteCopy(), bpp::LUDecomposition< Real >::piv, and bpp::NumConstants::SMALL().
Member Data Documentation
◆ L_
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private |
Definition at line 77 of file LUDecomposition.h.
Referenced by bpp::LUDecomposition< Real >::getL().
◆ LU
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private |
Definition at line 76 of file LUDecomposition.h.
Referenced by bpp::LUDecomposition< Real >::det(), bpp::LUDecomposition< Real >::getL(), bpp::LUDecomposition< Real >::getU(), bpp::LUDecomposition< Real >::LUDecomposition(), and bpp::LUDecomposition< Real >::solve().
◆ m
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private |
Definition at line 79 of file LUDecomposition.h.
Referenced by bpp::LUDecomposition< Real >::det(), bpp::LUDecomposition< Real >::getL(), bpp::LUDecomposition< Real >::LUDecomposition(), and bpp::LUDecomposition< Real >::solve().
◆ n
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private |
Definition at line 79 of file LUDecomposition.h.
Referenced by bpp::LUDecomposition< Real >::det(), bpp::LUDecomposition< Real >::getL(), bpp::LUDecomposition< Real >::getU(), bpp::LUDecomposition< Real >::LUDecomposition(), and bpp::LUDecomposition< Real >::solve().
◆ piv
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private |
Definition at line 81 of file LUDecomposition.h.
Referenced by bpp::LUDecomposition< Real >::getPivot(), bpp::LUDecomposition< Real >::LUDecomposition(), bpp::LUDecomposition< Real >::permuteCopy(), and bpp::LUDecomposition< Real >::solve().
◆ pivsign
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private |
Definition at line 80 of file LUDecomposition.h.
Referenced by bpp::LUDecomposition< Real >::det(), and bpp::LUDecomposition< Real >::LUDecomposition().
◆ U_
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private |
Definition at line 78 of file LUDecomposition.h.
Referenced by bpp::LUDecomposition< Real >::getU().
The documentation for this class was generated from the following file:
- Bpp/Numeric/Matrix/LUDecomposition.h
